Solving Multistep Equations

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What is a multistep equation?

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A multistep equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

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What does it mean to isolate a variable in an equation?

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Isolating a variable means rearranging the equation so that the variable is on one side of the equation by itself, making it easier to solve.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

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How do you solve the equation 3x + 15 = 3(x + 5)?

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First, apply the distributive property: 3x + 15 = 3x + 15. Then, subtract 3x from both sides to get 15 = 15, which shows there are infinitely many solutions.

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What is the first step to solve the equation 0.5(2x-6)=0.2(4x-10)?

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The first step is to distribute the constants: 0.5 * 2x - 0.5 * 6 = 0.2 * 4x - 0.2 * 10, which simplifies to x - 3 = 0.8x - 2.

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How do you clear fractions in an equation?

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To clear fractions, multiply every term in the equation by the least common denominator (LCD) of all the fractions present.

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What is the solution to the equation 4 - 2(x - 3) = 24?

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First, distribute: 4 - 2x + 6 = 24. Combine like terms: 10 - 2x = 24. Then, isolate x to find x = -7.

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What does it mean if an equation has no solution?

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An equation has no solution if the variable cancels out and results in a false statement, such as 0 = 5.

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What is an example of an equation with infinitely many solutions?

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An example is 2x + 4 = 2(x + 2). After simplification, both sides are equal, indicating infinitely many solutions.

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